
section1.7plus.5Introduction
Let \({Z}_K\)  denote the ring of algebraic integers of an algebraic number field \(K\) . Let degree of \(K\)  equal to \(n\)  over the field \({Q}\)  of rational numbers. The problem of computation of a \({Z}\) -basis of \({Z}_K\)  (called an integral basis of \(K\) ) is in general a difficult task and has attracted the attention of many mathematicians (cf. [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}). In 1900, Dedekind [2]} gave an explicit integral basis for pure cubic fields. In 1910, Westlund [10]} described an integral basis for pure prime degree number fields. In 1984, Funakura [3]} provided an integral basis of all pure quartic fields. In 2015, Hameed and Nakahara [5]} determined an integral basis of those pure octic fields \({Q}(\@root 8 \of {a})\) , where \(a\)  is squarefree integer. In 2017, Gaál and Remete [4]} gave an integral basis of \({Q}(\@root n \of {a})\) , where the integer \(a\)  is squarefree and \(3\le n\le 9.\)  Recently, Jakhar [6]} provided an explicit integral basis of number fields of the type \({Q}(\@root p_1p_2 \of {a})\) , where \(p_1, p_2\)  are distinct prime numbers.
